Nonlinear Sciences > Exactly Solvable and Integrable Systems

Abstract: From a 'discrete' functional zero curvature equation, functional
representations of (matrix) Burgers and potential KP (pKP) hierarchies (and
others), as well as corresponding Backlund transformations, can be obtained in
a surprisingly simple way. With their help we show that any solution of a
Burgers hierarchy is also a solution of the pKP hierarchy. Moreover, the pKP
hierarchy can be expressed in the form of an inhomogeneous Burgers hierarchy.
In particular, this leads to an extension of the Cole-Hopf transformation to
the pKP hierarchy. Furthermore, these hierarchies are solved by the solutions
of certain functional Riccati equations.